Something missing
There is something missing here. Aeroplanes and engine behaviour is predictable.
I remember flying a chieftain for the RFDS some years ago. We used to keep the main (inboard) tanks full, and the outboard tanks half full. On one ocasion I was flying along happily, using the outboard tanks for cruise, when I noticed the right tank guage reading about three quarters full, when it had only been half full when I took off. It kept increasing as I burned fuel.
I snagged the guage on the MR, and talked to our engineers about it. They checked it and found nothing wrong. It did it again on the next flight, and I talked to the engineers about it. They found nothing. We both walked away mumbling to ourselves. When I checked the aircraft and refuelled it on the ground, it behaved normally. But it did it again in flight. I asked the engineers to check the venting system. They said it was ok. It did it again, in flight and everyone thought I was nuts.
Finally, the engineers fitted a new seal to the fuel filler cap, and everything returned to normal.
I believe suction from the low pressure area where the fuel cap is, was sucking the bladder up so it lifted the float and increased the fuel guage reading. When the aircraft was on the ground for a while, the pressure equalised, and the symptoms were gone. Maybe the vent was partially restricted as well.
This may appear to be un connected to the 172 story, but there is a connection, and it is this. There IS A REASON why this happened to the 172, and it should be found. There is no black magic. The reason may be obscure, but it is there somewhere.
"Don't ever trust fuel guages" is a copout. They would not be fitted if they were no good. If they are well maintained they are useful. Many are not well maintained, and fluctuate too much. Pilots have let aircraft run out of fuel when the fuel guages have been telling them it was about to happen, and they "did not trust the fuel guages". Like everything else in aviation you double check. Using dipsticks and fuel records is normal good practise. In the case of this 172, the fuel guages warned the pilot, and he took appropriate action.